06 comp ball toss

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Physics with Vernier 6 - 1

Ball Toss

When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its

path. The ball then speeds up on its way back down. A graph of its velocity vs. time would showthese changes. Is there a mathematical pattern to the changes in velocity? What is theaccompanying pattern to the position vs. time graph? What would the acceleration vs. time graphlook like?

In this experiment, you will use a Motion Detector to collect position, velocity, and accelerationdata for a ball thrown straight upward. Analysis of the graphs of this motion will answer thequestions asked above.

OBJECTIVES

Collect position, velocity, and acceleration data as a ball travels straight up and down. Analyze the position vs. time, velocity vs. time, and acceleration vs. time graphs. Determine the best fit equations for the position vs. time and velocity vs. time graphs. Determine the mean acceleration from the acceleration vs. time graph.

MATERIALS

computer Vernier Motion DetectorVernier computer interface volleyball or basketballLogger Pro wire basket

PRELIMINARY QUESTIONS

1. Think about the changes in motion a ball will undergo as it travels straight up and down.Make a sketch of your prediction for the position vs. time graph. Describe in words what thisgraph means.

2. Make a sketch of your prediction for the velocity vs. time graph. Describe in words what thisgraph means.

3. Make a sketch of your prediction for the acceleration vs. time graph. Describe in words whatthis graph means.

PROCEDURE

1. Connect the Vernier Motion Detector to the DIG/SONIC 1 channel of theinterface. If the Motion Detector has a switch, set it to Normal.

2. Place the Motion Detector on the floor and protect it by placing a wire basket over it.

3. Open the file 06 Ball Toss from the Physics with Vernierfolder.

4. In this step, you will toss the ball straight upward above the Motion Detector and let it fall


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6 - 2 Physics with Vernier

back toward the Motion Detector. This step may require some practice. Hold the ball directlyabove the Motion Detector. Click to begin data collection. You will notice a clickingsound from the Motion Detector. Wait one second, then toss the ball straight upward. Be sureto move your hands out of the way after you release it. A toss of 0.5 m above the MotionDetector works well. You will get best results if you catch and hold the ball above the MotionDetector.

5. Examine the position vs. time graph. Repeat Step 4 if your position vs. time graph does notshow an area of smoothly changing position. Check with your teacher if you are not surewhether you need to repeat the data collection.

ANALYSIS

1. Either print or sketch the three motion graphs. The graphs you have recorded are fairlycomplex and it is important to identify different regions of each graph. Click the Examinebutton, , and move the mouse across any graph to answer the following questions. Recordyour answers directly on the printed or sketched graphs.

a) Identify the region when the ball was being tossed but still in your hands:

Examine the velocity vs. time graph and identify this region. Label this on the graph. Examine the acceleration vs. time graph and identify the same region. Label the graph.

b) Identify the region where the ball is in free fall:

Label the region on each graph where the ball was in free fall and moving upward. Label the region on each graph where the ball was in free fall and moving downward.

c) Determine the position, velocity, and acceleration at specific points.

On the velocity vs. time graph, decide where the ball had its maximum velocity, just as theball was released. Mark the spot and record the value on the graph.

On the position vs. time graph, locate the maximum height of the ball during free fall. Markthe spot and record the value on the graph.

What was the velocity of the ball at the top of its motion? What was the acceleration of the ball at the top of its motion?

2. The motion of an object in free fall is modeled byy = v0t+ gt2, wherey is the vertical

position, v0 is the initial velocity, tis time, and g is the acceleration due to gravity (9.8 m/s2).

This is a quadratic equation whose graph is a parabola. Your graph of position vs. timeshould be parabolic. To fit a quadratic equation to your data, click and drag the mouse acrossthe portion of the position vs. time graph that is parabolic, highlighting the free-fall portion.

3. Click the Curve Fit button, , select Quadratic fit from the list of models and click .Examine the fit of the curve to your data and click to return to the main graph.

4. How closely does the coefficient of the t2

term in the curve fit compare to g?

5. The graph of velocity vs. time should be linear. To fit a line to this data, click and drag themouse across the free-fall region of the motion. Click the Linear Fit button, .

6. How closely does the coefficient of the t term in the fit compare to the accepted value for g?

7. The graph of acceleration vs. time should appear to be more or less constant. Click and dragthe mouse across the free-fall section of the motion and click the Statistics button, .


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Ball Toss

Physics with Vernier 6 - 3

8. How closely does the mean acceleration value compare to the values ofg found in Steps 4and 6?

9. List some reasons why your values for the balls acceleration may be different from theaccepted value for g.

EXTENSIONS

1. Determine the consistency of your acceleration values and compare your measurement ofg tothe accepted value of g. Do this by repeating the ball toss experiment five more times. Eachtime, fit a straight line to the free-fall portion of the velocity graph and record the slope ofthat line. Average your six slopes to find a final value for your measurement of g. Does thevariation in your six measurements explain any discrepancy between your average value andthe accepted value ofg?

2. The ball used in this lab is large enough and light enough that a buoyant force and airresistance may affect the acceleration. Perform the same curve fitting and statistical analysistechniques, but this time analyze each half of the motion separately. How do the fitted curvesfor the upward motion compare to the downward motion? Explain any differences.

3. Perform the same lab using a beach ball or other very light, large ball. See the questions in #2above.

4. Use a smaller, more dense ball where buoyant force and air resistance will not be a factor.Compare the results to your results with the larger, less dense ball.

5. Instead of throwing a ball upward, drop a ball and have it bounce on the ground. (Position theMotion Detector above the ball.) Predict what the three graphs will look like, then analyze theresulting graphs using the same techniques as this lab.

6. Repeat your quadratic and linear curve fits to the position graphs but use the time offset

option in the general curve fit dialog. Interpret the constant and linear terms of the quadraticfit. What do they signify? What are the units of each term?

7. Repeat the linear fit to the velocity graph but use the general curve fit button, . In thatdialog, choose the linear fit and enable the time offset option. Interpret the y-intercept of thelinear fit. What does it signify? What are its units?


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Vernier Lab Safety Instructions Disclaimer

THIS IS AN EVALUATION COPY OF THE VERNIER STUDENT LAB.

This copy does not include:

z Safety information

z Essential instructor background information

z Directions for preparing solutions

z Important tips for successfully doing these labs

The complete Physics with Vernierlab manual includes 35 labs and essential teacherinformation. The full lab book is available for purchase at:http://www.vernier.com/cmat/pwv.html

Vernier Software & Technology13979 S.W. Millikan Way Beaverton, OR 97005-2886

Toll Free (888) 837-6437 (503) 277-2299 FAX (503) [email protected] www.vernier.com

06 comp ball toss

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